@article{b0629a2fbe434a11aaca82ccca41904d,
title = "End-point maximal L1 -regularity for the Cauchy problem to a parabolic equation with variable coefficients",
abstract = "We consider maximal L1-regularity for the Cauchy problem to a parabolic equation in the Besov space B˙p,10(Rn) with 1 ≤ p≤ ∞. The estimate obtained here is not available by abstract theory of the class of unconditional martingale differences, because the end-point Besov space is included. We consider the end-point estimate and show that the optimality of maximal regularity in L1 for the linear parabolic equation with variable coefficients.",
keywords = "75C05, Primary 35Q05, Secondary 35L60",
author = "Takayoshi Ogawa and Senjo Shimizu",
note = "Funding Information: The authors would like to thank the anonymous referees for pointing out mistakes in the first version of the manuscript and providing many helpful suggestions. All the comments have improved the present paper considerably. Thanks are also due to Professor Masashi Misawa and Professor Jan Pr{\"u}ss for their helpful comments on the variable coefficient case, and to Professor Tsukasa Iwabuchi for discussions on maximal regularity in the modulation spaces []. The work of the first author is partially supported by JSPS, Grant-in-Aid for Scientific Research S #25220702. The work of the second author is partially supported by JSPS, Grant-in-Aid for Scientific Research B #24340025 and the Alexander von Humboldt Foundation. Publisher Copyright: {\textcopyright} 2015, Springer-Verlag Berlin Heidelberg.",
year = "2016",
month = jun,
day = "1",
doi = "10.1007/s00208-015-1279-8",
language = "English",
volume = "365",
pages = "661--705",
journal = "Mathematische Annalen",
issn = "0025-5831",
publisher = "Springer New York",
number = "1-2",
}